This is based off memory, so correct me if I am wrong.
If I remember correctly, the Lands of Intrigue have a flavor similar to the Constantine Roman Empire, around the area of Turkey or so. This is where Europe started to blend in with Muslim type cultures, such as the Moors and such. (I could be wrong about the specific names, but I remember it is supposed to be a blend of European and Eastern cultures) The Lands of Intrigue are to the south, such as Amn and Tethyr. The Lands of Intrigue also venerate Tyr as a deity of that region.
That could explain why there is a "Mosque of Tyr". You may want to take a look of Lands of Intrigue, since it may go more into depth about the church of Tyr. It can be downloaded from the WotC website.